Comparing Investments

Lesson 37 Mathematics Assessment Project Formative Assessment Lesson Materials Comparing Investments MARS Shell Center University of Nottingham & UC Berkeley Alpha Version Please Note: These materials are still at the alpha stage and are not expected to be perfect. The revision process concentrated on addressing any major issues that came to light during the first round of school trials of these early attempts to introduce this style of lesson to US classrooms. In many cases, there have been very substantial changes from the first drafts and new, untried, material has been added. We suggest that you check with the Nottingham team before releasing any of this material outside of the core project team. If you encounter errors or other issues in this version, please send details to the MAP team c/o map.feedback@mathshell.org. 01 MARS University of Nottingham

Comparing Investments Teacher Guide Alpha Version January 01 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 8 9 30 31 3 33 34 35 36 37 38 39 40 41 Comparing Investments Mathematical goals This lesson unit is intended to help you assess how well students are able to interpret exponential and linear functions and in particular to identify and help students who have the following difficulties: Translating between descriptive, algebraic, tabular data, and graphical representation of the functions. Recognizing how, and why a quantity changes per unit interval. To achieve these goals students work on simple and compound interest problems. Common Core State Standards This lesson involves mathematical content in the standards from across the grades, with emphasis on: A-SSE: Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. F-LE: Construct and compare linear and exponential models and solve problems. Interpret expressions for functions in terms of the situation they model. This lesson involves a range of mathematical practices, with emphasis on: 1. Make sense of problems and persevere in solving them.. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. Introduction The lesson unit is structured in the following way: Before the lesson, students work individually on the assessment task Making Money? designed to reveal their current understandings and difficulties when working with linear and exponential functions. You then review their work, and create questions for students to answer in order to improve their solutions. After a whole-class introduction, students work in small groups on a collaborative matching cards task. In a plenary discussion, students review the main mathematical concepts of the lesson. Students return to their original task, consider their own responses, and then use what they have learned to complete a similar task. Materials required Each individual student will need: Copies of the assessment tasks Making Money? and Making Money?(Revisited), a calculator, a miniwhiteboard, a pen, and an eraser. Each small group of students will need A copy of Card Set A: Investment Plans and Formulae, Card Set B: Graphs, Card Set C: Tables, and Card Set D: Statements. A large sheet of poster paper, a marker, and a glue stick. There are some projector resources to help introduce activities and support whole-class discussion. Time needed Approximately 0 minutes before the lesson, a one-hour lesson and 0 minutes in a follow-up lesson (or for homework.) Timings given are only approximate. Exact timings will depend on the needs of your class. 01 MARS University of Nottingham 1

4 43 44 45 46 47 48 49 50 51 5 53 54 55 56 57 58 59 60 61 6 63 64 65 66 67 68 69 70 71 7 73 74 75 76 77 78 79 80 81 8 Comparing Investments Teacher Guide Alpha Version January 01 Before the lesson Assessment task: Making Money? (0 minutes) Have the students do this task, in class or for homework, a day or more before the lesson. This will give you an opportunity to assess their work, and to find out the kinds of difficulties students have with it. You will then be able to target your help more effectively in the follow-up lesson. Give each student a copy of the assessment task, Making Money? Introduce the task briefly, and help the class to understand the context. Why do we put money in a bank? [To keep it safe and gain interest.] What does interest mean? [The money the bank adds to the investment.] What is an interest rate? [This is the percentage by which the money grows each year. This is often called the APY Annual Percentage Yield ] Can you see why the $00 in Simply Savings grows to $0 after one year? Spend fifteen minutes on your own, reading through the questions and trying to answer them as carefully as you can. It is important that students are allowed to answer the questions without your assistance, as far as possible. Students should not worry too much if they cannot understand or do everything, because in the next lesson they will engage in a similar task, which should help them. Explain to students that by the end of the next lesson, they should expect to be able to answer questions like these confidently. This is their goal. Assessing students responses Making Money? Mary is going to invest some money. She sees two advertisements: Simply Savings Bank Simple interest rate: 10% per year. Compound Capital Bank Compound interest rate: 8% per year. 1. Mary invests $00 in each bank. Use a calculator to figure how much she will have in each bank at the end of each year. Show all your work. at Simply Savings in dollars Value at Compound Capital in dollars 0 00.00 00.00 1 0.00 Collect student s responses to the task, and make some notes on what their work reveals about their current levels of understanding. The purpose of doing this is to forewarn you of any difficulties students will experience during the lesson itself, so that you may prepare carefully. We suggest that you do not score students work. The research shows that this will be counterproductive, as it will encourage students to compare their scores, and will distract their attention from the mathematics. Instead, you can help students to make progress by asking questions that focus attention on aspects of their work. Some suggestions for these are given on the next page. These have been drawn from common difficulties in trials of this unit. We suggest that you write your own list of questions, based on your own students work, using the ideas that follow. You may choose to write questions on each student s work. If you do not have time to do this, select a few questions that will help the majority of students. These can then be displayed on the board at the end of the lesson. 3 4 5. Which of the graphs below best shows how Mary s money will grow in each bank? Graph A Graph B Graph C Value of Mary's money Years after Mary invests $00 Value of Mary's money Years after Mary invests $00 Value of Mary's money (a) The growth of her money at Simply Savings is best shown by graph!!!!!!! (b) The growth of her money at Compound Capital is best shown by graph!!!!!!! (c) If you think that none of these graphs are a good description, explain why below: Years after Mary invests $00 01 MARS University of Nottingham

Comparing Investments Teacher Guide Alpha Version January 01 Common issues: Student assumes simple interest for both investments (Q1, Q) For example: Student makes the Compound Capital investment grow by $16 per year. Student selects graph B for both banks (Q) Student figures out the interest on $100 (Q1) For example: Student writes that the Year 1 value of the savings at Compound Capital as $08. Student write a general formula (Q3) For example : A = P + RP n 100 or A = P " 1 + R % $ ' # 100 & Student writes the formula incorrectly (Q3) For example: A = 00 + 10n; A = 00 10n (Simply Savings.) A = 00 + 1.08 n ; A = 00 8n (Compound Capital.) Student assumes that Simply Savings will always be a better investment (Q4) Inefficient method (Q4) For example: Instead of using a formula, the student compounds the interest each year. Completes the task The student needs an extension task. Suggested questions and prompts: Can you explain the difference between compound interest and simple interest?? For the investment in Compound Capital, what is the amount in the bank at the end of year 1? What will be the interest after 1 year? Can you explain why the interest changes for year? What is 8% of $00? Can you write a formula that includes the interest rates for each of the banks? How can you check your answer? Try substituting values of n into your formula to check your answers. Which is the better investment after 5 years? Which is the better investment after 6/7/8 years? How do you know? What will happen to the difference in amounts over a longer period of time? Can you think of a quicker method for calculating the amount of money in the bank after say, 10 years? How long would it take each savings plan to double your investment? Does this doubling time depend on the size of the initial investment? Why, or why not? What would Mary get from each plan if she took out her money after 6 months? 83 84 01 MARS University of Nottingham 3

85 86 87 88 89 90 Comparing Investments Teacher Guide Alpha Version January 01 Suggested lesson outline Whole-class interactive introduction (10 minutes) Give each student a calculator, a mini-whiteboard, a pen, and an eraser. Today we will investigate two ways to invest money: simple interest and compound interest. What is the difference between simple and compound interest? To introduce simple interest, show the first slide of the projector resource. Odd One Out? Investment 1 $100 Simple Interest Rate: 5% Investment $400 Simple Interest Rate: 5% 91 9 93 94 95 96 97 98 99 100 101 10 103 104 105 106 107 108 109 110 111 11 Investment 3 $00 Simple Interest Rate: 10% Look at these three investments. Which is the odd one out? Write down your reasoning on your mini-whiteboards. Ask one or two students to explain their answers. Most students will answer that Investment 3 is the odd one out because it has a different interest rate. Prompt them to consider other possibilities: I think Investment 1 is the odd one out. Why do I think this? [Investment 1 will increase by $5 a year, whereas Investments and 3 will both increase by $0 a year.] Ask students to explain their answers. If students are struggling to answer the question, ask: Investment 1 and have the same interest rate, does this mean the investments will increase by the same amount each year? How much will each investment increase by each year? Now ask the students to represent the description of an investment algebraically. How can you represent Investment as formula? Start the formula with A =..., A is the amount in the bank. Use n to represent the number of years the money is invested. Allow students a few minutes to think about the question individually and then they should discuss the problem with a partner before sharing ideas with the whole class. (We sometimes refer to this as the think-pair-share strategy). Ask students to show you their formulae using their mini-whiteboards. Ask students with different answers to justify them. Encourage the rest of the class to challenge these explanations. You may find some students write the formula using a variable for the amount invested: e.g. A = P + 0.05Pn Can you substitute the value for P into your formula? Or, use interest rate in their formula, instead of interest: e.g. A = 400 + 5n or A = 400 + 0.05n 01 MARS University of Nottingham 4

Comparing Investments Teacher Guide Alpha Version January 01 113 114 115 Can you use your formula to figure out how much is in the bank after 5 years? Can you check this answer by using the description of the investment plan? To introduce compound interest, show Slide of the projector resource. Odd One Out Investment 1 A = 500! 1.06 4 Investment A = 50! 1.06 Investment 3 A = 500! 1.03 116 117 118 119 10 11 1 13 14 15 16 17 18 19 130 131 13 133 134 135 136 137 In each expression, A shows the value of an amount of money that has been invested for a given period of time. How do you know that these represent compound interest, not simple interest? What does each expression mean? Which is the odd one out? Write down you reason on your mini-whiteboards. Encourage students to discuss this, then ask a few with different answers to justify them. Students may reason that: Investment 1 is the odd one out because the money is invested over a longer period than the other two investments. Investment is the odd one out because the initial investment is different from the other two investments. Investment 3 is the odd one out because the interest rate is different from the other two investments. Try to make sure that students can see the significance of each number in the expressions by asking specific questions: What is the initial investment? How long is the money invested for? What is the interest rate? Encourage students to justify their answers. Look out for students that assume the interest rate is 1.06% or 1.03%. Can you use your calculators to work out the amount of money in each investment, after the specified period? [Investment 1: A = $631.4; Investment : A = $80.90; Investment : A = $530.45.] 138 139 01 MARS University of Nottingham 5

Comparing Investments Teacher Guide Alpha Version January 01 140 141 Collaborative activity 1: Card Set A: Investment Plans and Formulae (10 minutes) Organize students into groups of two or three. Give each group Card Set A: Investment Plans and Formulae. You have two sets of cards, one with descriptions of investment plans and one with the formulae. Some of the investment plans use simple interest and some use compound interest. Using what you have learned from our discussion, take it in turns to match a formula with a corresponding investment plan. There are two spare investment plan cards. Write on the blank cards the formula for these two plans. Some students may not be able to match all the cards. Later in the lesson they will be given more cards that should help them complete all the matches. P1 P3 P5 F1 F3 F5 Card Set A: Investment Plans and Formulae Simple Interest Rate: 16% Simple Interest Rate: 8% Compound Interest Rate: 8% A = 400 x 1.08 n A = 400 x 1.0 n P P4 P6 F F4 F6 Compound Interest Rate: % Investment: $00 Compound Interest Rate: % Simple Interest Rate: % A = 400 + 3n A = 400 + 8n 14 143 144 145 146 147 148 149 150 151 15 153 154 155 156 157 158 159 160 161 16 163 164 165 Note different student approaches to the task and support student reasoning Listen and watch students carefully, and in particular, listen to see whether they are addressing the difficulties they experienced in the assessment. You can use this information to focus the whole-class discussion towards the end of the lesson. Try not to make suggestions that move students towards a particular approach to the task. Instead, ask questions that help students to clarify their thinking. If the whole class is struggling on the same issue, write relevant questions on the board and hold a mini-discussion. It is important that students are encouraged to engage with their partner s explanations, and take responsibility for their partner s understanding. Pippa, you matched these two cards. Gita, can you explain why Pippa matched these cards? Encourage students to think about how the formulae relate to the investment plans: [Select a formula card.] For each year, will the interest change or remain the same? How can you check your answer is correct? Can you explain what the number 400 relates to in this formula? How can you work out the amount in the bank for this investment plan/formula after say, 3 years? [Select a formula card.] If you substitute a value for n, into this formula what do you get? [Select an investment plan card of a simple interest investment.] How can you calculate the interest made each year for this plan? How is this represented in a formula? [Select a formula card.] What can you tell me about the interest rate or the interest for this investment? Some students may assume that for simple interest, the interest added each year is the coefficient of n. What does 3 represent in this formula? [Card F: the interest.] How can you check this? Is this the same as the interest rate? 01 MARS University of Nottingham 6

Comparing Investments Teacher Guide Alpha Version January 01 166 167 168 169 170 171 What is the formula for an investment of $100 and a simple interest rate of 8%? How can you check that your answer is correct? How does the formula change if the investment is $00/$400? Collaborative activity : Card Sets B and C: Graphs and tables (15 minutes) As the groups finish matching the cards give them Card Sets B and C: Graphs and Tables. These cards should help students check their existing matches. Card Set B: Graphs Card Set C: Tables G1 G T1 T &!! % %!! $ $!! #" $ $#" % %#" '!! &! %! $! (" ' '(" # #(" 1 43.00 466.56 3 4 544.0 5 587.73 0 00.00 1 04.00 3 1.4 4 16.49 5 0.8 G3 G4 T3 T4 '%! '$! ' '!! &! %! $! (" ' '(" # #(" '!! &! %! $! ' # ( $ 1 408.00 3 44.00 4 43.00 5 440.00 1 408.00 3 44.48 4 43.97 5 441.63 G5 '! G6 &!! T5 T6 &! %! $! # $ % & % %!! $ $!! #" $ $#" % %#" 1 43.00 464.00 3 4 58.00 5 560.00 1 464.00 3 59.00 4 656.00 5 70.00 01 MARS University of Nottingham S-5 17 173 174 175 176 177 178 179 180 181 18 183 184 185 186 187 188 Now match the graphs and tables cards with the cards already matched. You must also calculate the missing value in each table. Observe the different strategies that students use as they do this and encourage them to try different methods and to draw links between the different representations. Try to avoid making all the connections for the students. Some may think about the shapes of the graphs or the differences between rows in the tables: Can you separate these graphs and tables into those that represent simple interest and those that represent compound interest? [Some are linear and some are exponential] Which investments go up by equal amounts each year and which go up by increasing amounts each year? How does the plan/formula/table/graph show this? What does this tell you about the investment plan? Some students in trials called the non-linear curves quadratic. You may need to help them distinguish between quadratic and exponential functions. Some students may substitute into an equation (e.g. n = 0 or n = 5), and check if the answer matches a point on one of the graphs. John you used substitution to calculate the value of the investment after 5 years. Can you now think of a different method? [Students could compare slopes of two graphs.] Some students may assume that the slope represents the interest rate. 01 MARS University of Nottingham 7

Comparing Investments Teacher Guide Alpha Version January 01 189 190 191 19 193 194 195 196 197 198 199 00 01 0 03 04 05 06 [Select a linear graph card.] What does the slope of this graph represent? [The interest added each year. The slope can be calculated by multiplying the simple interest rate by the amount invested.] When students have completed the task, ask them to check their work against that of a neighboring group. Check to see which matches are different from your own. If there are differences, ask for an explanation. If you still don't agree, explain your own thinking. You may then need to consider whether to make any changes to your own work. It is important that everyone in both groups understands the math. You are responsible for each other's learning. Collaborative activity 3: Card Set D: Statements (15 minutes) Give each group Card Set D: Statements, a large sheet of paper for making a poster, and a glue stick. In your groups you are now going to match one of these statements to the cards already on your desk. Card S1 matches two sets of cards. Encourage students to check their matches. For example, if students use graphs to match the statements, ask: Chris, you used this graph card to match the statement. Can you now use a different card to check your pairing is correct? When students have completed the task, ask them to check their work against that of a neighboring group. Once you have investigated the statement and are happy with your findings, stick the statement and investment plans on the poster. Add reasons for your all your matches. You may need to explain to students that the phrase 'Return for your money' means the interest gained for each 100 originally invested. Whole-class discussion (10 minutes) Organize a whole-class discussion about different strategies used to match the cards. You may first want to select a set of cards that most groups matched correctly. This approach may encourage good explanations. Then select one or two cards that most groups found difficult to match. Ask other students their views on which method is easiest to follow, as well as contributing ideas of alternative approaches. If there is time, then you may like to consider the following extension: Double your money. Show Slide 3 of the projector resource. S1 S3 S5 These two investments will take the same time to double your money. This investment gives the worst return for your money over two years or more. This investment is the best one over 0 years. Card Set D: Statements S S4 This investment will double your money in 1 years 6 months. This investment is the best one over 10 years. 01 MARS University of Nottingham 8

Comparing Investments Teacher Guide Alpha Version January 01 Double Your Money Investment 1 A = 500! 1.06 n Investment A = 50! 1.06 n Investment 3 Which two investments will take exactly the same time to double the money? A = 500! 1.03 n 07 08 09 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 At the start of the lesson, we noted that Investment 1 and Investment 3 invest the same amount of money, and Investment 1 and have same interest rate. Now try to answer the question [Investments 1 and will double the money in the same time, as they have the same interest rate.] Ask students to write their answers on their mini-whiteboards. After a few minutes ask students with different answers to justify them. Encourage other students to challenge their explanations. Does it matter how much money is invested? [No.] How can you answer the question without doing any calculations? In order to double your money, what should 1.06 n equal? [] Show me two different compound investment plans that take the same time to double your money. Show me two different compound interest investment plans that take different times to double your money. Which one would double your money first? How do you know? Students who are confident using the formula could be encouraged to provide an algebraic solution. For example, to show that doubling any amount of money takes the same amount of time, writing the starting amount as x and the final amount as x gives the equation (1.06 n )x = x, the x s cancel out, leaving the same equation to be solved each time (1.08 n = ). Some students may ask how to find the value of n. If you have time, and you think your students will understand, you may want to explain how logarithms can be used to make n the subject of the equation. Now show Slide 4 of the projector resource. Double Your Money Investment 1 A = 500 + 0n Investment A = 00 + 8n Investment 3 Which two investments will take exactly the same time to double the money? A = 00 + 0n 7 8 9 30 31 For Investment 1, what is the value of A when the initial investment is doubled? Does the time it takes to double your money depend on how much money is invested? [The time it takes to double your money for simple interest investments = Amount Invested Interest. If the interest rates are the same, then it does not matter how much money is invested.] 01 MARS University of Nottingham 9

Comparing Investments Teacher Guide Alpha Version January 01 3 33 34 35 36 37 38 39 40 41 4 43 44 45 46 47 Can you think of a quick way to answer the question? Show me two different simple interest investment plans that take the same time to double your money. Show me two different simple interest investment plans that take different times to double your money. Which one would double your money first? How do you know? Follow-up lesson: Revisiting Making Money? and reflecting on learning (0 minutes) Return to the students their original assessment task, and a copy of Making Money? (Revisited). Look at your original responses and think about what you have learned this lesson. If you have not added questions to individual pieces of work, then write your list of questions on the board. Students should select from this list, only the questions they think are appropriate to their own work. Using what you have learned, try to answer the questions on the new task Making Money? (Revisited). If you find you are running out of time, you could set this task in the next lesson or for homework. Extension One natural extension to this work would be to consider how much an investment will pay if it is withdrawn part way through a year. This leads to a consideration of the continuity of the growth function. For example, if the annual compound interest rate is 8%, then: 1 Approximate value after n years = A" (1.08) n = A" (1.08 1 ) 1n Replacing 1n by m, this gives : Value after m months = A" (1.0064) m 01 MARS University of Nottingham 10

48 49 50 51 5 53 54 55 56 57 58 59 60 61 6 63 Comparing Investments Teacher Guide Alpha Version January 01 Solutions Assessment Task: Making Money? 1.. (a) The growth of her money at Simply Savings is best shown by graph B (b) (c) Years Value at Simply Savings Value at Compound Capital 0 00.00 00.00 1 0.00 16.00 40.00 33.8 3 60.00 51.94 4 80.00 7.10 5 300.00 93.87 The growth of her money at Compound Capital is best shown by graph A Students may reason that if the interest is only added at the end of the year, then the graph would have discrete steps. These graphs assume that interest is added continuously. 3. A = 00 + 0n; A = 00 1.08 n. 4. For the first five investment years Simply Savings Bank is the better plan, however at the end of Year 7 Compound Capital starts to perform better ($34.76 compared to $340.) Compound Capital is a better investment for savers wanting to invest for 7 years or more. 64 65 66 67 68 69 70 71 7 73 74 75 76 77 78 79 Assessment Task: Making Money? (Revisited) 1.. (a) The growth of her money at Compound Investments is best shown by graph C (b) Years Value at Compound investments Value at Simple investments 0 300.00 300.00 1 315.00 318.00 330.75 336.00 3 347.9 354.00 4 364.65 37.00 5 38.88 390.00 The growth of her money at Simple investments is best shown by graph B (c) Students may reason that if the interest is only added at the end of the year, then the graph would have discrete steps. These graphs assume that interest is added continuously. 3. A = 300 1.05 n ; A = 300 + 18n. 4. For the first five investment years Simple Investments is the better plan, however at the end of Year 9 Compound investments starts to perform better ($465.40 compared to $46.00) Compound Investments is a better investment scheme for savers wanting to invest for 9 years or more. 80 81 01 MARS University of Nottingham 11

Comparing Investments Teacher Guide Alpha Version January 01 8 83 Collaborative Activity The highlighted parts are to be provided by the student. P1 Simple Interest Rate: 16% P Compound Interest Rate: % F6 A = 400 + 64n F3 A = 400 x 1.0 n G6 G4 &!! % %!! $ $!! '!! &! %! $! #" $ $#" % %#" ' # ( $ T6 1 464.00 58.00 3 59.00 4 656.00 5 70.00 T4 1 408.00 416.16 3 44.48 4 43.97 5 441.63 S4 This investment is the best one over 10 years. S1 (P and P4) These two investments will take the same time to double your money. P3 Simple Interest Rate: 8% F A = 400 + 3n G3 '%! '$! ' '!! &! %! $! (" ' '(" # #(" T5 1 43.00 464.00 3 496.00 4 58.00 5 560.00 S This investment will double your money in 1 years 6 months. P4 Investment: $00 Compound Interest Rate: % P5 Compound Interest Rate: 8% F5 A = 00 x 1.0 n F1 A = 400 x 1.08 n G5 G1 '! &! %! $! &!! % %!! $ $!! # $ % & #" $ $#" % %#" T 0 00.00 1 04.00 08.08 3 1.4 4 16.49 5 0.8 T1 1 43.00 466.56 3 503.88 4 544.0 5 587.73 S1 (P and P4) These two investments will take the same time to double your money. S5 This investment is the best one over 0 years. P6 Simple Interest Rate: % F4 A = 400 + 8n G '!! &! %! $! (" ' '(" # #(" T3 1 408.00 416.00 3 44.00 4 43.00 5 440.00 S3 This investment gives the worst return for your money over two years or more. 84 01 MARS University of Nottingham 1

Comparing Investments Student Materials Alpha Version January 01 Making Money? Mary is going to invest some money. She sees two advertisements: Simply Savings Bank Simple interest rate: 10% per year. Compound Capital Bank Compound interest rate: 8% per year. 1. Mary invests $00 in each bank. Use a calculator to figure how much she will have in each bank at the end of each year. Show all your work. at Simply Savings in dollars Value at Compound Capital in dollars 0 00.00 00.00 1 0.00 3 4 5. Which of the graphs below best shows how Mary s money will grow in each bank? Graph A Graph B Graph C Value of Mary's money Value of Mary's money Value of Mary's money Years after Mary invests $00 Years after Mary invests $00 Years after Mary invests $00 (a) The growth of her money at Simply Savings is best shown by graph (b) The growth of her money at Compound Capital is best shown by graph (c) If you think that none of these graphs are a good description, explain why below: 01 MARS University of Nottingham S-1

Comparing Investments Student Materials Alpha Version January 01 3. Write down a formula for calculating the amount of money in each of these banks after n years. 4. Mary wants to invest some money for 5 years or more. Which bank should she choose? Give full reasons for your answer. 01 MARS University of Nottingham S-

Comparing Investments Student Materials Alpha Version January 01 Making Money? (revisited) Jack is going to invest some money. He sees two advertisements: Compound Investments Compound interest rate: 5% per year. Simple Investments Simple interest rate: 6% per year. 1. Jack invests $300 in each scheme. Use a calculator to figure how much he will have in each scheme at the end of each year. Show all your work. at Compound Investments ($) Value at Simple investments ($) 0 300.00 300.00 1 3 4 5. Which of the graphs below best shows how Jack s money will grow in each bank? Graph A Graph B Graph C Value of Jack's money Value of Jack's money Value of Jack's money Years after Jack invests $300 Years after Jack invests $300 Years after Jack invests $300 (a) The growth of his money at Compound Investments is best shown by graph (b) The growth of his money at Simple investments is best shown by graph (c) If you think that none of these graphs are a good description, explain why below: 01 MARS University of Nottingham S-3

Comparing Investments Student Materials Alpha Version January 01 3. Write down a formula for calculating the amount of money in each of these schemes after n years. 4. Jack wants to invest some money for 5 years or more. Which scheme should he choose? Give full reasons for your answer. 01 MARS University of Nottingham S-4

Comparing Investments Student Materials Alpha Version January 01 Card Set A: Investment Plans and Formulae P1 Simple Interest Rate: 16% P Compound Interest Rate: % P3 Simple Interest Rate: 8% P4 Investment: $00 Compound Interest Rate: % P5 Compound Interest Rate: 8% P6 Simple Interest Rate: % F1 F A = 400 x 1.08 n A = 400 + 3n F3 F4 A = 400 x 1.0 n A = 400 + 8n F5 F6 01 MARS University of Nottingham S-5

Comparing Investments Student Materials Alpha Version January 01 Card Set B: Graphs G1 G &!! '!! % %!! $ $!! &! %! $! #" $ $#" % %#" (" ' '(" # #(" G3 G4 '%! '$! ' '!! &! %! $! (" ' '(" # #(" '!! &! %! $! ' # ( $ G5 G6 '! &!! &! %! $! % %!! $ $!! # $ % & #" $ $#" % %#" 01 MARS University of Nottingham S-6

Comparing Investments Student Materials Alpha Version January 01 Card Set C: Tables T1 T 1 43.00 466.56 3 4 544.0 5 587.73 0 00.00 1 04.00 3 1.4 4 16.49 5 0.8 T3 T4 1 408.00 3 44.00 4 43.00 5 440.00 1 408.00 3 44.48 4 43.97 5 441.63 T5 T6 1 43.00 464.00 3 4 58.00 5 560.00 1 464.00 3 59.00 4 656.00 5 70.00 01 MARS University of Nottingham S-7

Comparing Investments Student Materials Alpha Version January 01 Card Set D: Statements S1 S These two investments will take the same time to double your money. This investment will double your money in 1 years 6 months. S3 S4 This investment gives the worst return for your money over two years or more. This investment is the best one over 10 years. S5 This investment is the best one over 0 years. 01 MARS University of Nottingham S-8

Odd One Out? Investment 1 $100 Simple Interest Rate: 5% Investment $400 Simple Interest Rate: 5% Investment 3 $00 Simple Interest Rate: 10% Alpha Version January 01 01 MARS University of Nottingham Projector resources: 1

Odd One Out? Investment 1 A = 500 1.06 4 Investment A = 50 1.06 Investment 3 A = 500 1.03 Alpha Version January 01 01 MARS University of Nottingham Projector resources:

Double Your Money Investment 1 A = 500 1.06 n Investment A = 50 1.06 n Investment 3 Which two investments will take exactly the same time to double the money? A = 500 1.03 n Alpha Version January 01 01 MARS University of Nottingham Projector resources: 3

Double Your Money Investment 1 A = 500 + 0n Investment A = 00 + 8n Investment 3 Which two investments will take exactly the same time to double the money? A = 00 + 0n Alpha Version January 01 01 MARS University of Nottingham Projector resources: 4